Hoa Bui wrote:
> Dear all,
>
> Please help me with this problem:
>
> I have a series of points:
> In[9]:=points
> Out[9]={{0.0001,0.359381},{0.0002866,0.403984},{0.000821394,0.454122},{0.00235411,0.510482},{0.00674688,0.573838},{0.0193365,0.645056}}
>
> Define one of my function as the trapezoidal area created by these
> points up to some x:
> linNx = Interpolation[points, InterpolationOrder -> 1];
> ff[x_] := Integrate[linNx[s], {s, 0.0001, x}]
>
> Define the second function as a power law:
> gg[x_] := 0.9 x^(1/0.9)
>
> My third function is the root of the equation:
> hh[x_] := FindRoot[ff[y] == gg[x], {y, 0.0001, 0.019}];
>
> I can evaluate h at specific values of x, e.g. h[0.001] ({y ->
> 0.00107654}), h[0.01] ({y -> 0.0101302}), etc...
>
> Now say I want to use hh[x] in an integral,
> NIntergrate[hh[x],{x, 0.0001, 0.019}]
> obviously it doesn't work, and I have tried using Solve instead of
> FindRoot but it also did not output a numerical value for the integral
> because the inverse function is not in closed form or something..
>
> Is there a way for me to compute the integral of hh[x] ?
>
> Thank you all so much,
> Hoa Bui
Here is the other part you asked for:
sol3=Flatten@NDSolve[hhh'@y==(x@y/.sol)&&hhh@points[[1,1]]==0,hhh,
{y,points[[1,1]],points[[-1,1]]}]